# 529-0003-00L Advanced Quantum Chemistry

Semester | Autumn Semester 2018 |

Lecturers | M. Reiher, S. Knecht |

Periodicity | yearly recurring course |

Language of instruction | English |

Comment | Only for Chemistry MSc, Programme Regulations 2005. |

Abstract | Advanced, but fundamental topics central to the understanding of theory in chemistry and for solving actual chemical problems with a computer. Examples are: * Operators derived from principles of relativistic quantum mechanics * Relativistic effects + methods of relativistic quantum chemistry * Open-shell molecules + spin-density functional theory * New electron-correlation theories |

Objective | The aim of the course is to provide an in-depth knowledge of theory and method development in theoretical chemistry. It will be shown that this is necessary in order to be able to solve actual chemical problems on a computer with quantum chemical methods. The relativistic re-derivation of all concepts known from (nonrelativistic) quantum mechanics and quantum-chemistry lectures will finally explain the form of all operators in the molecular Hamiltonian - usually postulated rather than deduced. From this, we derive operators needed for molecular spectroscopy (like those required by magnetic resonance spectroscopy). Implications of other assumptions in standard non-relativistic quantum chemistry shall be analyzed and understood, too. Examples are the Born-Oppenheimer approximation and the expansion of the electronic wave function in a set of pre-defined many-electron basis functions (Slater determinants). Overcoming these concepts, which are so natural to the theory of chemistry, will provide deeper insights into many-particle quantum mechanics. Also revisiting the workhorse of quantum chemistry, namely density functional theory, with an emphasis on open-shell electronic structures (radicals, transition-metal complexes) will contribute to this endeavor. It will be shown how these insights allow us to make more accurate predictions in chemistry in practice - at the frontier of research in theoretical chemistry. |

Content | 1) Introductory lecture: basics of quantum mechanics and quantum chemistry 2) Einstein's special theory of relativity and the (classical) electromagnetic interaction of two charged particles 3) Klein-Gordon and Dirac equation; the Dirac hydrogen atom 4) Numerical methods based on the Dirac-Fock-Coulomb Hamiltonian, two-component and scalar relativistic Hamiltonians 5) Response theory and molecular properties, derivation of property operators, Breit-Pauli-Hamiltonian 6) Relativistic effects in chemistry and the emergence of spin 7) Spin in density functional theory 8) New electron-correlation theories: Tensor network and matrix product states, the density matrix renormalization group 9) Quantum chemistry without the Born-Oppenheimer approximation |

Lecture notes | A set of detailed lecture notes will be provided, which will cover the whole course. |

Literature | 1) M. Reiher, A. Wolf, Relativistic Quantum Chemistry, Wiley-VCH, 2014, 2nd edition 2) F. Schwabl: Quantenmechanik für Fortgeschrittene (QM II), Springer-Verlag, 1997 [english version available: F. Schwabl, Advanced Quantum Mechanics] 3) R. McWeeny: Methods of Molecular Quantum Mechanics, Academic Press, 1992 4) C. R. Jacob, M. Reiher, Spin in Density-Functional Theory, Int. J. Quantum Chem. 112 (2012) 3661 Link 5) K. H. Marti, M. Reiher, New Electron Correlation Theories for Transition Metal Chemistry, Phys. Chem. Chem. Phys. 13 (2011) 6750 Link 6) K.H. Marti, M. Reiher, The Density Matrix Renormalization Group Algorithm in Quantum Chemistry, Z. Phys. Chem. 224 (2010) 583 Link 7) E. Mátyus, J. Hutter, U. Müller-Herold, M. Reiher, On the emergence of molecular structure, Phys. Rev. A 83 2011, 052512 Link Note also the standard textbooks: A) A. Szabo, N.S. Ostlund. Verlag, Dover Publications B) I. N. Levine, Quantum Chemistry, Pearson C) T. Helgaker, P. Jorgensen, J. Olsen: Molecular Electronic-Structure Theory, Wiley, 2000 D) R.G. Parr, W. Yang: Density-Functional Theory of Atoms and Molecules, Oxford University Press, 1994 E) R.M. Dreizler, E.K.U. Gross: Density Functional Theory, Springer-Verlag, 1990 |

Prerequisites / Notice | Strongly recommended (preparatory) courses are: quantum mechanics and quantum chemistry |